Various sensor systems for measuring the position ϕ of a rotating or linearly moving position indicator are known, in which the information to be obtained is represented by sine and cosine shaped varying raw signals p1=cos(ϕ) and p2=sin(ϕ). Possible implementations include e.g. the measurement of components of the induction field of a permanent magnet at suitable locations in space. The searched position is then determined from p1, p2 e.g. via the function ϕ=a tan 2(p2,p1) by means of the function a tan 2 known from the C-programming language. These prerequisites severely restrict possible arrangements of sensor elements and position indicator, and in particular require a high degree of accuracy in their production or the relative positioning of the sensor chip and the position indicator, respectively.
A fundamental difficulty with these methods is that a non-ideal arrangement of the position indicator and the sensor chip leads to distortions of the raw signals, in particular that these no longer have the pure sine and cosine shape and thus lead to an inaccurate determination of the position ϕ. There exist methods to improve the raw signal quality, e.g. by using offset and amplitude corrections. A method for a sensor arrangement with two sensors known from WO 2005124286 is based on a description of the measuring points as ellipses and requires specific calibration measurements, which provide parameters for the corrections and which can be realized in practice only with considerable effort. This method requires great care in the design of the sensor arrangement and especially in the adjustment of the permanent magnet, so that the measured values lie sufficiently precisely on an ellipse. If the actual rotational axis does not pass through the magnetically defined center of the permanent magnet, the correction can even cause the opposite effect of an increase in the angular error.
In many instances, a position sensing system is responsive to external fields (e.g., the earth's magnetic field in the case of a position indicator based on permanent magnets). Without countermeasures, these additional field components cannot be distinguished from the useful field so that the external fields restrict the accuracy of the position measuring system.
A fundamental challenge for position measuring systems is their long-term stability, i.e., an initially sufficiently accurate calibration changes over time, e.g. by mechanical displacement of the components relative to one another or by drifting of electronic sensor properties. However, the measurement quality of systems during normal operation is not ascertainable according to the state of the art, in particular this cannot take place intrinsically, i.e. without reference measurements from outside. However, an intrinsic method would be of great importance for fault-tolerant systems. In addition, a recalibration of a position measuring system during normal operation would be very valuable in order to decisively improve the long-term stability.